can someone help me with geometry pls?

Question

I have this question: In a regular polygon each int. angle is 108 greater than each ext. angle. find the number of sides. We must use these formulae pls: sum of int=(n-2)180 or sum of extermal angles=360. Pls show all steps.

Answer 1

The first thing you need to determine is the measure of each interior angle or exterior angle. According to your problem, each interior angle is 108 degrees greater than each exterior angle. Thus,



x - measure of each exterior angle

x + 108 - measure of each interior angle



Since the interior and exterior angle form a linear pair, then we have



x + x + 108 = 180

2x = 72

x = 36



Thus, the measure of each exterior angle is 36 degrees.



Now, we know that the total measure of all exterior angles should add up to 360. Since we have a regular polygon here, then we have equal measures for all exterior angles. We have



n * 36 = 360

n = 10



Thus, your [regular] polygon has 10 sides, or is a decagon.



Hope this helps!!!!!

Answer 2

Since we all know that internal angle + external angle at any point makes 180 degrees.



Take a random point, say M, we have and call m1, m2 its int./ext. angles

m1 + m2 = 180

m1 = m2 + 108

=> 2*m2 + 108 = 180 => m2 = 72/2 = 36

=> m1 = 36 + 108 = 144



I don't know if the two formulae you gave are correct (they most likely are).

m2 = one external angle

sum of all external angles = 360* => total number of external angles = 360/36 = 10

Since there are 10 external angles, there are 10 (logically?) points/sides in this polygon.

Answer 3

enable the size be x cm. which ability the width is x - 15 because of fact that's 15cm shorter. additionally, the fringe of a rectangle is: length + length + width + width = P merely replace the size and width with the values from earlier: x + x + (x - 15) + (x - 15) = P the fringe is given as 350cm so: x + x + (x - 15) + (x - 15) = 350 team the x's jointly and additionally the 15: 4x - 30 = 350 flow the 30 to the different component: 4x = 380 Divide each little thing with the help of four to get x with the help of itself: x = 380/4 = ninety 5 x = ninety 5 ============================= The length, x, is 95cm The width is x - 15 (ie. ninety 5 - 15) so that's 80cm. subsequently, the size are: ninety 5 x 80